{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CY4YTCDCPBFEAFYOC2UWJF4VBM","short_pith_number":"pith:CY4YTCDC","schema_version":"1.0","canonical_sha256":"1639898862784a40170e16a96497950b3b9d7da6ee82a7a83835771f37acc6a5","source":{"kind":"arxiv","id":"1510.08797","version":3},"attestation_state":"computed","paper":{"title":"Convexity in Tree Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO","q-bio.PE"],"primary_cat":"math.MG","authors_text":"Bernd Sturmfels, Bo Lin, Ruriko Yoshida, Xiaoxian Tang","submitted_at":"2015-10-29T17:46:55Z","abstract_excerpt":"We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all \\ ultrametrics. The ${\\rm CAT}(0)$-metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric behave better. They exhibit properties desirable for geometric statistics, such as geodesics of small depth."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.08797","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-10-29T17:46:55Z","cross_cats_sorted":["cs.CG","math.CO","q-bio.PE"],"title_canon_sha256":"6dd42ff291082920eab0b99dc39f5834c13ee9e417eb5461d01d52f6bb8efb13","abstract_canon_sha256":"83f39db76aaaf315e4420627b5e14c45d15f5e32be4647d87d8b6c740cf0abc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:14.662379Z","signature_b64":"GuEjEsyBbXCYHSPSV3fuYoAvvIir0k4joNfUqAYkkuWKzbdi+ovZ3liQzHayPsLGFySRu6Hs42wAkh3iVV8/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1639898862784a40170e16a96497950b3b9d7da6ee82a7a83835771f37acc6a5","last_reissued_at":"2026-05-18T00:23:14.661686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:14.661686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convexity in Tree Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO","q-bio.PE"],"primary_cat":"math.MG","authors_text":"Bernd Sturmfels, Bo Lin, Ruriko Yoshida, Xiaoxian Tang","submitted_at":"2015-10-29T17:46:55Z","abstract_excerpt":"We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all \\ ultrametrics. The ${\\rm CAT}(0)$-metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric behave better. They exhibit properties desirable for geometric statistics, such as geodesics of small depth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08797","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.08797","created_at":"2026-05-18T00:23:14.661799+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.08797v3","created_at":"2026-05-18T00:23:14.661799+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08797","created_at":"2026-05-18T00:23:14.661799+00:00"},{"alias_kind":"pith_short_12","alias_value":"CY4YTCDCPBFE","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CY4YTCDCPBFEAFYO","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CY4YTCDC","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM","json":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM.json","graph_json":"https://pith.science/api/pith-number/CY4YTCDCPBFEAFYOC2UWJF4VBM/graph.json","events_json":"https://pith.science/api/pith-number/CY4YTCDCPBFEAFYOC2UWJF4VBM/events.json","paper":"https://pith.science/paper/CY4YTCDC"},"agent_actions":{"view_html":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM","download_json":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM.json","view_paper":"https://pith.science/paper/CY4YTCDC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.08797&json=true","fetch_graph":"https://pith.science/api/pith-number/CY4YTCDCPBFEAFYOC2UWJF4VBM/graph.json","fetch_events":"https://pith.science/api/pith-number/CY4YTCDCPBFEAFYOC2UWJF4VBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM/action/storage_attestation","attest_author":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM/action/author_attestation","sign_citation":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM/action/citation_signature","submit_replication":"https://pith.science/pith/CY4YTCDCPBFEAFYOC2UWJF4VBM/action/replication_record"}},"created_at":"2026-05-18T00:23:14.661799+00:00","updated_at":"2026-05-18T00:23:14.661799+00:00"}